Regression analysis | Mathematics homework help

Question 1 Assignment: Data needed for questions 3-7 at bottom of page:

In a regression analysis with multiple dependent variables, multicollinearity can be caused by:

A strong nonlinear relationship between the dependent variable and one or more independent variables.

A strong heteroskedastic relationship between the dependent variable and one or more independent variable.

A strong linear relationship between two or more independent variables.

None of the above.

Question 2 
Market researcher Ally Nathan is studying the relationships among price, type (classical or steel string), and consumer demand for acoustic guitars. She wants to find the relationship between demand and price, controlling for type.
To determine this relationship, she should

Run a simple regression of the dependent variable demand on the independent variable price and observe the coefficient on price. 

Run a simple regression of the dependent variable demand on the independent variable type and observe the coefficient on type. 

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on type. 

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on price. 

Question 3 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
The coefficient on the independent variable tells us that:

For every additional dollar of GDP, average energy consumption increased by 3,786 trillion BTUs.

For every additional trillion dollars of GDP, average energy consumption increased 3,786 BTUs. 

For every additional trillion BTUs of energy consumption, average GDP increased by $3,786 trillion. 

For every additional trillion dollars of GDP, average energy consumption increased by 3,786 trillion BTUs. 

Question 4 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
Which of the following statements is true?

The y-intercept of the regression line is 62,695 trillion BTUs. 

The x-intercept of the regression line is $62,695 trillion.

In the event that a thermonuclear war completely halts all economic activity and the US GDP drops to zero, energy consumption will sink to 62,695 trillion BTUs. 

None of the above. 

Question 5 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”. 
In a given war, if GDP is $7.4 trillion, expected energy consumption is:

Around 91,501 trillion BTUs

Around 90,711 trillion BTUs 

Around 28,016 trillion BTUs

Around 467,729 trillion BTUs.

Question 6 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
How much of the variation in energy consumption can be explained by variation in the gross domestic product?

About 99.99%

About 97%

About 94%

Almost none of the variation in energy consumption can be explained by variation in GDP. 

Question 7 
The data table at the bottom of the page tabulates a pizza paror’s advertising expenditures and sales for 8 consecutive quarters. The marketing manager wants to know how much of an impact current advertising will have on sales two quarters from now.
While running a regression with the dependent variable “sales” and the independent variable “advertising lagged by two quarters”, how many data points can she use, given the available data?

9

For questions 3 through 6:
Year GDP 
(in $trillions) Car Gas Mileage (in mpg) Energy Consumption 
( in trillions of BTU)
1980 2.796 16 78,435
1981 3.131 16.5 76,569
1982 3.259 16.9 73,441
1983 3.535 17.1 73,317
1984 3.933 17.4 76,972
1985 4.213 17.5 76,705
1986 4.453 17.4 76,974
1987 4.743 18 79,481
1988 5.108 18.8 82,994
1989 5.489 19 84,926
1990 5.803 20.2 84,567
1991 5.986 21.1 84,640
1992 6.319 21 86,051
1993 6.642 20.5 87,780
1994 7.054 20.7 89,571
1995 7.401 21.1 91,501
1996 7.813 21.2 94,521
1997 8.318 21.5 94,969
1998 8.782 21.6 95,338
1999 9.274 21.4 96,968

US Energy Consumption (in trillion BTUs)
vs. Gross Domestic Product ($trillions)

Regression Statistics
Multiple R 0.9709
R2 0.9426
Adjusted R2 0.9394 F test results
Standard Error 1,889 F value Signif. F
Observations 20 295.51 0.0000 

Coefficients Std Error t Stat P-value
Intercept 62,695 1,325 47.31 0.0000 
GDP ($trillions) 3,786 220 17.19 0.0000 

For Question #7:

Quarter Sales (in $) Advertising (in $)
Qtr 1, 2001 523,000 88,000
Qtr 2, 2001 512,000 84,000
Qtr 3, 2001 528,000 92,000
Qtr 4, 2001 533,000 92,000
Qtr 1, 2002 540,000 96,000
Qtr 2, 2002 540,000 95,000
Qtr 3, 2002 538,000 93,000
Qtr 4, 2002 541,000 98,000

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